(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that:

(|x+y|)/(1+|x+y|) ≤ ((|x|)/(1+|x|)) + ((|y|)/(1+|y|))

2. Relevant equations

You are given the triangle inequality:

|x+y| ≤ |x| + |y|

3. The attempt at a solution

(This is done from the result, as I haven't been able to find the starting point)

(|x+y|)/(1+|x+y|) ≤ (|x|(1+|y|)+|y|(1+|x|))/((1+|x|)(1+|y|))

(|x+y|)/(1+|x+y|) ≤ (|x|+2|x||y|+|y|)/(1+|x|+|y|+|x||y|)

This doesn't seem to go anywhere. I also tried flipping the whole thing to get:

(1+|x+y|)/(|x+y|)≤(1+|x|)/(|x|)+(1+|y|)/(|y|)

but this doesn't seem to lead anywhere either...

I'm not sure how to go about this problem.

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# Homework Help: Prove using the Triangle Inequality

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